WOLFRAM SYSTEM MODELER

## kc_twoPhaseOverall |

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`SystemModel["Modelica.Fluid.Dissipation.Utilities.SharedDocumentation.HeatTransfer.StraightPipe.kc_twoPhaseOverall"]`

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This information is part of the Modelica Standard Library maintained by the Modelica Association.

Calculation of local **two phase** heat transfer coefficient **kc_2ph** for (horizontal/vertical) **boiling** or (horizontal) **condensation** for an overall flow regime.

- circular cross sectional area
- no subcooled boiling
- film condensation

**Boiling in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.BoilHor):**

The local two phase heat transfer coefficient **kc_2ph** during boiling in a **horizontal** straight pipe for an overall regime is calculated according to *[Gungor/Winterton 1986, p.354, eq. 2]* :

kc_2ph = E_fc*E_fc_hor*kc_fc+S_nb+S_nb_hor*kc_nb

with

Bo=qdot_A/(mdot_A*dh_lv) | as boiling number [-], |

dh_lv | as evaporation enthalpy [J/kg], |

E_fc=f(Bo,Fr_l,X_tt) | as forced convection enhancement factor [-], |

E_fc_hor =f(Fr_l) | as forced convection enhancement factor for horizontal straight pipes [-], |

Fr_l | as Froude number assuming total mass flow rate flowing as liquid [-], |

kc_2ph | as local two phase heat transfer coefficient [W/(m2K)], |

kc_fc | as heat transfer coefficient considering forced convection [W/(m2K)], |

kc_nb | as heat transfer coefficient considering nucleate boiling [W/(m2K)], |

mdot_A | as total mass flow rate density [kg/(m2s)], |

qdot_A | as heat flow rate density [W/m2], |

Re_l | as Reynolds number assuming liquid mass flow rate flowing alone [-], |

S_nb =f(E_fc,Re_l) | as suppression factor of nucleate boiling [-], |

S_nb_hor =f(Fr_l) | as suppression factor of nucleate boiling for horizontal straight pipes [-], |

x_flow | as mass flow rate quality [-], |

X_tt = f(x_flow) | as Martinelli parameter [-]. |

**Boiling in a vertical pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.BoilVer):**

The local two phase heat transfer coefficient **kc_2ph** during boiling in a **vertical** straight pipe for an overall regime is calculated out of the correlations for boiling in a horizontal straight pipe, where the horizontal correction factors **E_fc_hor,S_nb_hor** are unity.

Please note that the correlations named above are not valid for subcooled boiling due to a different driving temperature for nucleate boiling and forced convection. At subcooled boiling there is no enhancement factor (no vapour generation) but the suppression factor remains effective.

**Condensation in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.CondHor):**

The local two phase heat transfer coefficient **kc_2ph** during condensation in a **horizontal** straight pipe for an overall regime is calculated according to *[Shah 1979, p.548, eq. 8]* :

kc_2ph = kc_1ph*[(1 - x_flow)^0.8 + 3.8*x_flow^0.76*(1 - x_flow)^0.04/p_red^0.38]

where the convective heat transfer coefficient **kc_1ph** assuming the total mass flow rate is flowing as liquid according to *[Shah 1979, p.548, eq. 5]* :

kc_1ph = 0.023*Re_l^0.8*Pr_l^0.4*lambda_l/d_hyd

with

d_hyd | as hydraulic diameter [m], |

kc_2ph | as local two phase heat transfer coefficient [W/(m2K)], |

kc_1ph | as convective heat transfer coefficient assuming total mass flow rate is flowing as liquid [W/(m2K)], |

lambda_l | as thermal conductivity of fluid [W/(mK)], |

pressure | as thermodynamic pressure of fluid [Pa], |

p_crit | as critical pressure of fluid [Pa], |

p_red = pressure/p_crit | as reduced pressure [-], |

Pr_l | as Prandtl number assuming [-], |

Re_l | as Reynolds number assuming total mass flow rate is flowing as liquid [-], |

x_flow | as mass flow rate quality [-], |

The local two phase heat transfer coefficient **kc_2ph** during for horizontal and vertical boiling as well as for horizontal condensation is shown for a straight pipe in the figures below.

**Boiling in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.BoilVer):**

Here the validation of the two phase heat transfer coefficient is shown for boiling in a horizontal straight pipe.

The two phase heat transfer coefficient (**kc_2ph**) w.r.t. *Gungor/Winterton* is shown in dependence of the mass flow rate quality (**x_flow**) for different mass flow rate densities (**mdot_A**). The validation has been done with measurement results from *Kattan/Thome* for R134a as medium.

The two phase heat transfer coefficient increases with increasing mass flow rate quality up to a maximum value. After that there is a rapid decrease of (**kc_2ph**) with increasing (**x_flow**). This can be explained with a partial dryout of the pipe wall for a high mass flow rate quality.

**Condensation in a horizontal pipe (target = Modelica.Fluid.Dissipation.Utilities.Types.TwoPhaseHeatTransferTarget.CondHor):**

Here the validation of the two phase heat transfer coefficient is shown for condensation in a horizontal straight pipe.

The two phase heat transfer coefficient (**kc_2ph**) w.r.t. *Shah* is shown in dependence of the mass flow rate quality (**x_flow**) for different mass flow rate densities (**mdot_A**). The validation has been done with measurement results from *Dobson/Chato* for R134a as medium.

- Bejan,A.:
**Heat transfer handbook**. Wiley, 2003.- M.K. Dobson and J.C. Chato:
**Condensation in smooth horizontal tubes**. Journal of HeatTransfer, Vol.120, p.193-213, 1998.- Gungor, K.E. and R.H.S. Winterton:
**A general correlation for flow boiling in tubes and annuli**, Int.J. Heat Mass Transfer, Vol.29, p.351-358, 1986.- N. Kattan and J.R. Thome:
**Flow boiling in horizontal pipes: Part 2 - new heat transfer data for five refrigerants.**. Journal of Heat Transfer, Vol.120. p.148-155, 1998.- Shah, M.M.:
**A general correlation for heat transfer during film condensation inside pipes**. Int. J. Heat Mass Transfer, Vol.22, p.547-556, 1979.